Republicans may be tired of all the baby coverage, but not the rest of the world. Britain continues to be front-page news around the globe this week. From the Deccan Chronicle in Bangalore, India, to the Pasadena Star-News, California, there are pictures of a beaming Duke and Duchess of Cambridge cradling their young son on the steps of the Lindo Wing.

Even La Nación, one of the newspapers that has vociferously staked Argentina’s claim to the Falkland Islands, has the Duke and Duchess on its front page, along with breathless prose about the Duchess’s poise and her polka dots.

It may seem odd that the world is so in thrall to Britain. Our finances have rarely been in such poor shape. Having slipped outside the top five economies in the world, overtaken by Brazil, most forecasters predict that our disposable income will be squeezed until well after the young prince starts primary school.

The Armed Forces are stretched to breaking point. We do not even have a fully fledged aircraft carrier at our disposal.

But experts believe that the House of Windsor – and especially the glamorous young Cambridge family with their new son, George – are responsible for the fact that our country is still held in such high esteem.

John Leech, a Liberal Democrat MP on the Culture, Media and Sport Select Committee, says: “It is quite amazing how the rest of the world is fascinated by our Royal family. You could argue the Royal family have never been so popular in Britain, but it is hard to underestimate quite what an attraction they are to overseas tourists.

“Many adored Diana, Princess of Wales, and I have no doubt that Kate, William and their new baby will do nothing but good for how Britain is seen from overseas.”

The fact that the Duke jumped into a British-made Range Rover, holding a Britax car seat (designed, if not made, in Britain) was a sign that Prince George of Cambridge will become the country’s youngest ambassador.

Richard Lim, at the British Retail Consortium, says: “The fact that there’s so much attention on the UK at the moment can only reinforce this notion that British brands are quality, upmarket brands, and that’s great for retailers operating internationally.”

David Haigh, the chief executive of consultancy firm Brand Finance, says: “In some ways Brand Britain has never been so strong – it is a stable, tolerant place and that has only been enhanced by the Royal family, which has softened and liberalised its approach.”

His company calculates the economic value of nations, as if they were a brand just like Heinz or Coca-Cola, using the same methodology used to account for the “intangible value” of companies above and beyond the worth of their factories and products. By Brand Finance’s reckoning, Britain increased its value again last year, though it remained in fifth place. What was interesting, however, was how much of that value was made up by the Queen and her family.

It calculated that the monarchy is worth £44.5 billion to the British economy, even after taking into account all the costs involved in funding it. Of that total, £26 billion was down to “intangible assets” – the goodwill the family generates, the tourists they bring in and the extra value a royal warrant gives to a company, especially an exporter.

This week, it calculated that the royal baby will be responsible for adding £521 million to the value of the economy – through a short-term boost in sales of memorabilia, and a longer-term uplift in consumer confidence.

The Cambridges embody what foreign policy wonks call “soft power”. Hard power is bullets and banknotes – how much clout the Ministry of Defence and the Foreign and Commonwealth office can wield. Soft power involves what in the old days would have been called “cultural relations” – touring Shakespeare around the Punjab, teaching English to the natives of Togoland, the Hollywood Cricket Club (whose secretary was one PG Wodehouse).

Britain may be short on bullets and banknotes, but it is doing extremely well at cultural relations.

Multiple strands of “made-in-Britain” culture are enthralling the rest of the world. Anyone who thought Britain’s sporting glory was an Olympics flash in the pan can think again. Over the past few weeks we have had images of Chris Froome wearing a sequin-encrusted yellow jersey atop a podium by the Arc de Triomphe, dominating European television screens, and Andy Murray’s victory at Wimbledon splashed not just on back pages but on front pages, too.

And don’t forget that James Bond stormed his way to the top of box offices around the globe at the end of last year, neatly reminding everyone of the efficacy of Savile Row tailoring. Even our interminable “Keep calm and carry on” merchandise has found its way on to shelves from Brazil to Malaysia.

In a recent survey published by Monocle magazine, Britain topped the poll for soft power nations, leaping from third place and knocking the US off the No 1 slot. The report said that the Olympic opening ceremony, in all its uplifting glory, heralded a new self-confident and modern country.

One of the most notable legacies of the Olympics was the confirmation that our affection for the Royal family, at rock bottom only 15 years ago, has returned to levels not seen since the Coronation. The public reception to the risky sketch in which the Queen “jumped” out of a helicopter underlined how fondly Britons feel towards their unelected, untarnished head of state.

Interestingly, the Windsors perform just as well in polls overseas, with the Queen among Americans having a 15-point higher rating than President Obama.

Those fighting on the front line in Britain’s cultural army, those who practise the dark art of “museum diplomacy” (“we’ll lend you a Holbein if you drop your trade sanctions”), say that the Royal family is an invaluable weapon.

The British Council is a rather quaint organisation founded by Sir Rex Leeper, a man who promoted the idea of “cultural propaganda” in the 1930s. Its main job now is to encourage people overseas to learn English and “engage” with the culture of Britain.

John Worne, director of strategy at the institution, says: “You can’t underestimate the Olympics’ impact in terms of a refresh and a restoring of the UK’s national image. But underpinning that is a very strong set of institutions: the British Council, the BBC World Service, the British Museum, the British Library – all of these in world terms are right at the top. And then you have the Royal family.

“It is a combination of the history, the pageantry and the sheer volume of hard work. They are out there on the ground all over the world, making a difference.”

Plenty of other European nations have colourful monarchies. But historians are clear about why the Mountbatten-Windsors, with their significant and public wealth, capture the imagination in a way that the Bourbons of Spain or Glücksburgs of Denmark do not.

“In our increasingly global age, Britain itself has come to symbolise 'history’ to the rest of the world,” says Kate Williams, author of Young Elizabeth. “We have this long, rich unbroken line stretching back, and the Royal family embodies that in a way that other royal families do not.

“It’s what people find particularly fascinating. The Windsors match the stereotype that the rest of the world has about Britain: posh, polite, living in the past and in castles.”

And in a world that laps up celebrities, William, Kate and their son are only going to become more important, says David Haigh.

“The media is now insatiable: with blogs and 24-hour internet, it needs feeding all the time. William and Kate are the perfect story. First they were a young couple in love, then there was the wedding, now there is the baby, who will get more attention than any other child in the world.”

Some may find the global coverage excessive – but it serves a need. Two generations after the Empire was dismantled, Prince George of Cambridge is keeping the Union flag flying abroad.